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Subtraction of Integers

Last updated date: 22nd Feb 2024
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What is Subtraction?

In order to fully understand the subtraction of integers, you first need to know what subtraction is. Subtraction is defined as one quantity being taken from another, which means that the two numbers are being "subtracted." The bigger number is called the minuend and the smaller number is called the subtrahend. In this article, we are going to learn about how to subtract integers and will see some of the integers examples.

Subtraction of Digits

Subtraction of Digits

Subtraction of Integers Definition

Subtraction of integers is a mathematical operation which is arithmetic in nature, and it involves the subtraction of two numbers. The objective of subtraction of integers is to find out how much bigger one number is than another or vice versa. It can be accomplished by subtracting the first integer from the second or by adding the difference between the two integers to a third integer.

The method of finding the difference between two integers is known as subtracting integers. Depending on whether the numbers are positive, negative, or a mix, the value may increase or decrease. Integer subtraction is an arithmetic operation that finds the difference between integers with the same or different signs.

Integers Rules

There are sure principles to be followed to subtract two numbers. Subtraction using an integers rules chart helps in understanding the sign convention. The guidelines for subtracting numbers are given below with integers examples:

Subtraction Using Integers Rules Chart

Subtraction Using Integers Rules Chart

Following are the rules for subtracting integers:

  • When we subtract 0 from any integer, the result is the integer itself.

  • We may discover the additive inverse or opposite of any integer by subtracting it from 0.

  • Integer subtraction is accomplished by changing the sign of the subtrahend. If both numbers have the same sign, we add their absolute values and append the common sign. If the absolute numbers have different signs, we find the difference and place the sign of the larger number in the result.

Subtracting Integers with the Same Sign

When we subtract two integers with the same sign, we subtract their absolute values and add the common sign. The absolute value of a number is the number's positive value. For example, the absolute value of 9 is 9, the absolute value of -9 is 9, and so on.

We modify the sign of the subtrahend when subtracting numbers. For example, -3-(-5) can be written as -3+5. The absolute value of 5 is 5, and -3 is now 3. We get 2 by subtracting 3 from 5. Because 5>3, the answer's sign will be the same as the sign of 5, which is positive. As a result, -3-(-5)=2.

Here, it is important to note that every subtraction fact can be written as an addition fact. For example, 2-4 is the same as 2+(-4).

More examples:

(-1) - (- 6) = - 1 + 6 = 5

3 - 8 = - 5

24 - 17 = 7

Subtracting Integers with Different Signs

When subtracting two integers with different signs, the sign of the subtracted integer is changed. Then, if both integers become positive, the outcome will be positive; if both integers become negative, the result will be negative. For example, if we want to subtract (-9) from 5, that is 5-(-9), we will change the sign of 9 and then add the integers, which means it will be 5+9=14. Therefore, 5-(-9)=14.

This can also be understood using another way in which the absolute values are added, and the sign of the minuend is attached to the result. For example, if we want to subtract (-9) from 5, first we find the absolute values of both. The absolute value of -9 is 9, and 5 is 5. Now, find the sum of these absolute values, which is 9+5=14. As 5 is the minuend with a positive sign, the answer sign will be positive. Therefore, 5-(-9)=14.

Solved Examples

Example 1: Subtract the given integers using the rules for subtracting integers.

Subtract $-56$ from $-90$

Ans: This question is based on subtracting two integers with the same sign. Here, if we write it in the form of an expression, we get $-90-(-56)$. This can be written as $-90 + 56$. Let us find the difference between the absolute values. So, 90 56 is 34. Since $90>56$, the answer sign will be the same as the sign of 90, which is negative. Therefore, $-90-(-56) = -34$.

Example 2: By using subtracting integers rules, find out which number should be added to 43 to get $-20$ as the answer.

Ans: Let $x$ be the number that should be added to 43 to get $-20$. So, we can form an equation in terms of $x$.

$x + 43 = -20$

To find the missing value, we need to solve the equation.

$x + 43 = -20$

$x = -20-43$

$x = -63$

Therefore, $-63$ has to be added to 43 to get $-20$.

Practice Problems

Q1. Find the value of (-1030) - 79. 

Ans: -1109

Q2. Find the value of (-1030) + (-38). 

Ans: -1068

Q3. Find the value of (-459) - (-38). 

Ans: -421


As far as we have learned about subtraction, i.e. subtraction is defined as one quantity being taken from another, which means that the two numbers are being "subtracted." Then we see how integers affect the subtraction due to a change in the sign. In the integer rule, we have learned that subtracting Integers with the same sign and subtracting Integers with different signs, both show different results. So in this way, we now have command over the subtraction of integers. 

FAQs on Subtraction of Integers

1. What is a general rule for subtracting integers on a number line?

The following principles define the subtraction of integers on a number line: 

  • Every subtraction fact can be stated as an addition fact.

  • To add a positive number, move to the right side (or the positive side) of the number line.

  • To add a negative integer, move to the left side (or the negative side) of the number line.

  • Any specified integers can be used as the starting point for travelling along the number line.

2. What is the role of subtraction?

Subtraction is the term used to describe how we 'take away' one or more numbers from another. Subtraction is also used to find the difference between two numbers. Subtraction is an important tool to help us find out what is left when taking one number away from another. For example, if Ram has 25 rupees and spends 15 rupees on a new shirt, we can use subtraction to find out how much money Ram has left.

3. How to subtract integers when we have two positive integers?

The rules for subtraction are similar to those for addition. If you've got two positive integers, you subtract the smaller number from the larger one. The result will always be a positive integer: 5 – 3 = 2.